Effects of different live feed on ballan wrasse (Labrus bergylta) larval hepatocyte and enterocyte development

Size: px
Start display at page:

Download "Effects of different live feed on ballan wrasse (Labrus bergylta) larval hepatocyte and enterocyte development"

Transcription

1 Effects of different live feed on lln wrsse (Lrus ergylt) lrvl heptocyte nd enterocyte development Mrte Romundstd Mrine Costl Development Sumission dte: Jnur 2015 Supervisor: Elin Kjørsvik, IBI Co-supervisor: Jn-Ove Evjemo, IBI Norwegin University of Science nd Technology Deprtment of Biology

2

3 Acknowledgements This mster thesis ws written t the Deprtment of Biology, t the Norwegin University of Science nd Technology (NTNU), under the guidnce of Professor Elin Kjørsvik t the Deprtment of Biology NTNU nd resercher Jn Ove Evjemo NTNU. The experimentl work ws crried out t the NTNU Centre of Fisheries nd Aquculture (Sel) nd in the lortories of SINTEF Fisheries nd Aquculture. This experiment ws prt of the reserch project Produksjon v erggylte (900554), funded y the Fishery nd Aquculture Industry Reserch Fund (FHF), collortion etween NTNU, SINTEF, Nofim, NIFES nd the Institute of Mrine Reserch, s well s lln wrsse juvenile nd slmon producers. I would like to thnk Elin Kjørsvik for her guidnce nd ptients in writing this thesis, Jn Ove Evjemo for the help nd guidnce in the first feeding experiment nd Tor Brdl for invlule help nd ssistnce in the l. I would lso like to thnk Od Skognes Høylnd nd Mri Stvrkki for gret collortion in the first feeding experiment, nd to Mren Rnheim Ggnt, Stine Wiorg Dhle nd Andres Hgemnn for ll the help with fish feeding nd live feed rering. Thnks to LAKS nd ll fellow students t Sel for gret converstions, fun prties nd good support during these lst two yers. I would lso like to thnk my fmily nd my oyfriend for ll their love nd support through the mster thesis process. Trondheim, Jnury 2015 Mrte Romundstd I

4 Astrct Slmon lice infesttions re one of the iggest chllenges for Norwegin slmon frming tody. Delousing gents hve een the solution to these infesttions in the pst, ut overuse nd wrong dosges hve cused the lice to ecome resistnt to the chemicls nd thus rendering them ineffective. As result clener fish hve een proposed s n ll-nturl delousing gent. The lln wrsse hs een proposed s the idel clener fish for Norwegin wters nd is eing cught in the wild nd put in the fish pens with the slmon. To e le to use lln wrsse on lrger scle nd in sustinle wy, it hs een proposed to egin frming of the lln wrsse. This will secure stle supply of this fish to the slmon frms. One of the keys to successfully rering lln wrsse is to figure out the idel feeding regime in the lrvl stge of development when the lrve re dependent on live feed. The trditionl live feed of rotifers nd rtemi do not meet the nutritionl requirements of mrine fish lrve nd hs to e enriched to meet these requirements. Copepods hs een suggested s more suitle live feed s it is the nturl prey of most wild mrine fish nd meets their nutritionl requirements thus not needing to e enriched. In this study the trditionl live feed of rotifers nd rtemi ws compred with using intensively rered copepods (Acrti tons) exclusively through the whole live feed period of lln wrsse lrve. The Rotifer-group ws fed enriched rotifers from 4 dph until 30 dph, nd ws co-fed enriched rotifers nd enriched rtemi etween 30 dph nd 40 dph. From 40 dph until the end of the experiment (45 dph) the Rotifer-group ws fed enriched rtemi exclusively. The Copepod-group ws fed intensively rered copepods exclusively throughout the experiment (4-45 dph). The lln wrsse lrve were fed Acrti tons nuplii until 15 dph, then s the lrve grew they were fed copepodits from 15 dph until 30 dph. From 30 dph to 45 dph the lrve were fed comintion of copepodits nd dult Acrti tons in 2:1 rtio. The two groups were compred to see if the nutritionl differences of the live prey hd n effect on different growth prmeters nd how it ffected the gut nd liver development in the lln wrsse lrve. The results from this study indictes tht intensively rered Acrti tons ws etter live feed for lln wrsse lrve compred to enriched rotifers nd enriched rtemi. The lrve tht were fed copepods showed etter growth nd hd etter liver nd gut development thn the lrve fed enriched rotifers nd rtemi. II

5 Contents 1 Introduction Bckground Slmon lice nd clener fish Blln wrsse nd live feed Gut nd liver development Aim of the study.4 2 Mterils nd methods First feeding experiment Live feed production Cultivtion nd hrvesting of microlge (Rhodomons ltic) Cultivtion of copepods (Acrti tons) Egg production Production of copepod nuplii for feed Cultivtion, enrichment nd hrvesting of rotifers (Brchionus sp.) Cultivtion of Artemi frnciscn Lrvl smpling nd fixtion Stndrd length nd myotome height Dry weight nd dily weight increse Survivl Histologicl nlysis Light microscope Trnsmission electron microscope Sttisticl nlysis 12 3 Results Growth nd survivl Dry weight nd dily weight increse Stndrd length (SL) nd myotome height (MH) Survivl Liver morphology Light microscopy Trnsmission electron microscopy Surfce re frction of heptocyte components Are size of nucleus nd mitochondri Mitochondril chrcteristics Gut morphology Light microscopy Trnsmission electron microscopy Surfce re frctions of enterocyte components Are size of nucleus nd mitochondri Mitochondril ppernce.37 III

6 3.3.6 Microvilli density nd height Discussion Lrvl growth nd development Effects of different live feed on lrvl heptocyte nd Enterocyte development Nuclei size nd ppernce Mitochondril development Endoplsmic reticulum Lipid nd glycogen storge Conclusion.46 References.47 Appendix 1.52 Emedding lln wrsse lrve in EPON 52 IV

7 1. Introduction 1.1 Bckground With the rising numer of people on the plnet, food production hs to e expnded to meet the future requirements nd quculture is sid to ply n importnt role is this development. Aquculture, especilly of slmon, hs ecome n importnt industry in Norwy. With production of 1.16 million tons of slmon in 2013 (Norwegin Directorte of Fisheries, 2014), it hs ecome n importnt industry in Norwy. The export of slmon from Norwy ws vlued t 40 illion NOK (Sttistics Norwy, 2014) mking it n importnt export. The slmon industry hs developed lot since the eginning in the 1970`s. The technologicl progress hs mde lrge scle fish frms possiility nd tody one fish frm cn contin fish (Trnger et l., 2014). Although these intensive fish frms re highly successful there re severl chllenges with high density fish rering. The spreding of diseses, the escpe of frmed slmon, which interfere with the wild slmon popultion, nd incresed numers of slmon lice in the Norwegin fjords, re some of the chllenges the industry fces tody (Trnger et l., 2014). 1.2 Slmon lice nd clener fish The slmon louse is n ectoprsite (Kt 1979) tht feeds on the skin of its host (Pike & Wdsworth, 2000). This dmges the skin of the slmon nd cuse lcertions tht cn ecome ftl, especilly when slmon is infected with lrge numer of lice (Grimnes & Jkosen, 1996). In ddition they cn infect the wild slmon nd cuse prolems for the wild popultions (Bjørn et l., 2001; Butler, 2002). The industry hs tried to comt this prolem for long time nd in the pst the min solution hs een to use delousing gents to remove the lice from the slmon. Overuse nd wrong dosges hve cused the lice to ecome resistnt to severl kinds of delousing remedies (Jones et l., 1992; Sevtdl & Horserg, 2003; Lees et l., 2008) nd it is now hrd to effectively get rid of the lice using just chemicls. A solution hs een to use wrsse nd other species of clener fish for delousing the frmed slmon. They cn e put into the pens with the slmon nd will et the lice off the fish. Wrsse hs een used s clener fish since the lte 1980`s (Espelnd et l., 2010), ut hs not een widely used until lter yers. In Norwegin wters the species tht is considered to e the most suited for this purpose is the lln wrsse. It hs ig ppetite, it will effectively clen the lice off the slmon (Ottesen et l., 2008), nd it is ctive t lower tempertures thn 1

8 other wrsse species (Kvenseth & Øien, 2009). As the chemicl delousing gents gets less nd less effective the more one hs to rely on the nturl delousing effects of the wrsse. Most of the wrsse used in Norwegin fish frms tody, re cught in the wild (Kvenseth et l., 2003), ut in longer perspective one hs to think of more sustinle wys of supplying the wrsse to the frms. Frming of lln wrsse would help relieve the pressure on the wild popultions nd help ensure stle supplies of wrsse to the slmon frms. 1.3 Blln wrsse nd live feed. When strting to frm new species there is severl chllenges nd needs for knowledge. How do we get the fish to reed in cptivity, wht is the est htching conditions, how ig re the lrve when they htch etc. One of the iggest chllenges with mrine fish lrve is their generl smll size t htching. The slmon is so developed t htching tht it cn e fed with formulted feed right wy, ut the smller lln wrsse is not s developed t htching nd therefore hs to e fed live feed (Conceico et l., 2010). The trditionl live feed regime used on severl mrine species, consists of first period of feeding with rotifers, nd s the lrve grows igger, they re wened on to the lrger rtemi, efore they re ig enough to e wened on to formulted feed (Southgte, 2003; Conceio et l., 2010). One of the chllenges with these species s food for the fish lrve is tht they do not nturlly meet the lrve s requirements for essentil ftty cids (EFAs). Therefore they hve to e enriched efore they re fed to the lrve (Evjemo & Olsen, 1997; Conceico et l., 2010). EFAs like eicospentenoic cid (20:5n-3; EPA), docoshexenoic cid (22:6n-3; DHA) nd rchidonic cid (20:4n-6; ARA) is sid to e prticulrly importnt for the growth nd development of mrine fish lrve (Srgent et l., 1999; Bell et l., 2003). Not only is the mount of these ftty cids importnt, ut the rtio etween them re lso importnt, the optiml rtio will vry from species to species (Srgent et l., 1999). EFAs stored in the polr lipid frction is sid to e more esily ville for the fish thn ftty cids stored in the neutrl lipids (Izquierdo et l., 2000; Gisert et l., 2005; Wold et l., 2009). When the rotifers nd rtemi re enriched, the essentil ftty cids re stored in the neutrl lipid frction (Rinuzzo et l., 1994; Rinuzzo et l., 1994; Nerhus, 2007) nd re therefore less ville for the developing lrve (Izquierdo et l., 2000; Kjørsvik et l., 2009; Wold et l., 2009). As n lterntive to the more trditionl live feed regime it hs een proposed to feed the lrve with copepods. Both nturlly hrvested nd intensively rered copepods hve een proven to e good live prey option for mrine fish lrve. When compred to feeding with rotifers nd rtemi, copepods s live feed hs resulted in etter growth, survivl nd pigmenttion 2

9 (Evjemo & Olsen, 1997; Luizi et l., 1999; Shields et l., 1999; Imslnd et l., 2006; Eidsvik, 2010). Copepods re the nturl pry of mny wild mrine fish lrve (Hunter, 1981) nd re more suited to meet the nutritionl requirements of the fish lrve. They do not need to e enriched s the mount nd rtio of essentil ftty cids meets the requirements nd is more ville to the lrve s it is stored in the polr lipid frction (Evjemo & Olsen, 1997; Evjemo et l., 2003; vn der Meeren et l., 2008; Overrein et l., 2010) 1.4 Gut nd liver development As mentioned mrine fish lrve like the lln wrsse re quite smll nd undeveloped t htching (Osse et l., 1997; Yufer & Dris, 2007). The mouth nd nus opens in time for exogenous feeding nd the gut itself is n undifferentited tue with no functionl stomch (Kjørsvik et l. 1991). As the lrve grow the gut will differentite nd will get more nd more developed over time (Yufer & Dris, 2007, Govni et l,. 1986; Wgø et l., 2001). The lln wrsse will never develop functionl stomch (Hmre & Sæle, 2011) nd therefor the functionl development of the gut is importnt for the lrve to e le to digest nd sor the required nutrients for growth nd survivl. The liver is not developed t htching nd ppers t the strt of exogenous feeding. It will grow over time s the fish lrve grows nd ecome more nd more developed (Hoehne- Reitn & Kjørsvik, 2004; Kjørsvik et l., 2004; Young et l., 2006). The liver ctolizes ft, crohydrtes nd protein nd stores energy like glycogen nd lipids (Lie et l., 1986; Young et l., 2006). The liver is esily ffected y mlnutrition or strvtion nd is good indictor of the nutritionl qulity of live feed (Hoehne-Reitn & Kjørsvik, 2004). 3

10 1.5 Aim of the study: The im of this study is to compre two different live feed progrms to see if using intensively rered copepods s live feed for lln wrsse lrve will give etter growth nd development thn the more trditionl live feed of enriched rotifers nd rtemi. We will hve two groups of three replics ech were one group is fed enriched rotifers nd then rtemi, while the other group is fed intensively rered copepods of incresing size exclusively throughout the experiment. To mesure ny difference etween the two groups we re looking t different growth prmeters s stndrd length, myotome height, dry weight nd dily weight increse. In terms of lrvl development we re going to look t the liver nd gut development of the two groups to see if the difference in nutritionl qulity of the live feed will give different development in the limentry system. In the liver nd gut we will look t re size of nuclei nd mitochondri, the re frction of nuclei, mitochondri nd glycogen, the generl ppernce of the liver nd gut tissue nd the ppernce of mitochondril memrnes nd criste. We will lso look t the microvilli density nd height in the gut. 4

11 2. Mterils nd methods 2.1 First feeding experiment. The first feeding experiment ws performed on lln wrsse lrve (Lrus ergylt) nd ws conducted in the CodTech l t NTNU Sel in Trondheim, Norwy. The experiment consisted of two different feeding regimes with three replictes of ech tretment. The first group (the Copepod-group) ws fed Acrti tons exclusively throughout the whole experiment. Strting with nuplii until 15 dys post htch (dph) then s the lrve grew they were fed copepodits from 15 until 30 dph. From 30 to 45 dph the lrve were fed comintion of copepodits nd dult Acrti Tons in 2:1 rtio. The other group (the Rotifer-group) were fed rotifers (Brchionus Sp.) enriched on Multigin (BioMr, Norwy) until 40 dph. From 30 to 40 dph the Rot group ws co-fed enriched rotifers nd enriched Brine Shrimp (Artemi frnciscn) efore the lrve were fed Brine shrimp exclusively until the end of the experiment. Blln wrsse lrve (Lrus ergylt) from Nofim (Sunndlsør, Norwy) ws plced in holding tnk with gentle ertion for cclimtiztion (12 C, 250 L) when they were 2 dph. The following dy (3 dph) the lrvl density ws mesured to get n estimted count of numer of lrve. The lrve were trnsferred to six 100 L conicl ottomed, cylindricl tnks with n estimted numer of 8200 lrve per tnk. From 2 dph to 4 dph the lrve were kept in drkness nd from 4 dph nd throughout the experiment the lrve were kept in constnt illumintion (MASTER TL-D 90 Grphic, 18W/965, Philips, Netherlnds). Temperture nd oxygen levels were mesured every dy (ProODO Opticl Dissolved Oxygen Meter, YSI Inc, OH, USA), eing kept t C (tle 2.1) nd 80 % sturtion respectively. The sewter tht ws pumped into the tnks, ws filtered through sndfilter nd through 1µm mesh to get rid of prticles (Skjermo et l. 1997), nd ws microilly mtured to stilize the cteril content. The wter exchnge ws grdully incresed from 2 to 8 times dy through the experiment. Cermic cly (Vingerling K148, Sielco, Germny) ws dded to the wter to increse the visul contrst nd reduce the cteril lod. With incresing wter exchnge the mount of cly dded to the wter ws incresed from 1.6 g per feeding t the eginning of the experiment to 3 g per feeding t the end of the experiment (tle 2.1). 5

12 Tle 2.1: Experimentl setup nd prmeters for the strt feeding experiment of lln wrsse lrve. Dys post htch Temperture ( C) Dy degrees ## Cly (g/ tnk /dy) - 3,2 4,8 7,5 8 8,5 9 Wter exchnge rte Feeding frequency 2 times dy 3 times dy Rotifer-group: 3 tnks Individuls per feeding - Individuls per feeding Enriched rotifers Enriched rtemi 3000 Copepod-group 3 tnks Copepods Individuls per feeding Stge n c n c n c 67 % c + 33 % 67 % n + 33 % N:nuplii, c:copepodits, : dult 6

13 2.2 Live feed production Cultivtion nd hrvesting of microlge (Rhodomons ltic) Rhodomons ltic (Clone NIVA 5/9 Cryptophyce: Pyrenomondles) were grown in 160 nd 200 litre plexigls cylinders. In periods of incresed production 300 litre plstic gs were lso used. The ph in the cylinders ws kept etween 7.5 nd 8.5 (ph/mv-meter, WTW ph 315i, Germny) nd the culture ws continuously erted with 1-2% CO 2. When overgrowing of the cylinder wlls ws oserved, the tnks were drined of lge nd clened with hot wter nd chlorine, nd then rinsed. To replenish the clened cylinder 50 % of the lge content of neighoring tnk ws trnsferred to the clen tnk, the cylinder filled to the top with sewter nd Conwy medium (1 ml per liter sewter) ws dded. The wter used in the lge cultivtion ws filtered through snd filter, heted to 20 C, nd filtered through 1 µm mesh, efore eing chlorinted (10-15% NOCl, 0.25 ml per litre, no ertion, >5 hours) nd dechlorinted (N 2 S 2 O 3, 3 g per 100 litre, ertion, >5 hours). 50 % of the lge in cylinder were hrvested dily. The remining culture ws diluted with sewter nd 1 ml Conwy medium per liter sewter ws dded Cultivtion of copepods (Acrti tons) Egg production Acrti tons (clone DFH.AT1) ws cultivted under constnt illumintion in three 1700 liter tnks, with flow through of sewter (snd filtered, heted to 20 C nd filtered through 1µm mesh) t wter exchnge rte of once per dy. The sieve covering the wter outlet ws clened every morning to keep the sieve from ecoming clogged. Temperture, O 2 levels, ph nd slinity ws mesured every morning (ProODO Opticl Dissolved Oxygen Meter, YSI Inc., OH, USA; LH-T28, Lohnd, Chin) nd kept t C, over 4 mg L-1 dissolved O 2, nd ppt respectively. Hrvested lge (Rhodomos ltic) were trnsferred to 1000 L tnk nd were fed continuously (Nesse, 2010) to the copepod tnks y n electromgnetic dosing pump (AXS602, Seko, Itly). The copepod eggs were collected dily y siphoning long the ottom of the tnks. The wter collected ws filtered through two sieves with 120 µm nd 100 µm mesh to rinse out ny wste, efore the wter ws filtered through 64 µm sieve to concentrte the eggs. The eggs were rinsed with sewter efore eing stored in sewter in NUNC EsyFlsks (Nunc A/S, Denmrk.) t 2 C. 7

14 Production of copepod nuplii for feed The mount of eggs needed ws emptied from NUNC flsk into 100 L white plstic tnks nd ws kept under moderte ertion nd t C. After 24 h when the eggs htched the nuplii were fed Rhodomons 3 times dy until hrvesting. When collecting the nuplii needed for feeding, the density ws estimted y tking out wter smple from the tnk, fixting the smple with Lugol`s solution nd tking out 7 drops of 50 µl. The individuls in ech drop were counted, the highest nd the lowest count ws cncelled nd the density ws estimted y clculting the men of the 5 remining drops. The desired mount ws hrvested nd concentrted y 64 µm sieve nd stored in 100 L plstic tnk under moderte ertion nd 8 C until they were fed to the lrve(>12 hours). Before feeding the nuplii density in the holding tnk ws estimted, the desired mount for one feeding ws tken out nd concentrted efore eing trnsferred to the lrvl tnks Cultivtion, enrichment nd hrvesting of rotifers (Brchionus sp.) Brchionus sp. ws cultured in three 250 L tnks with conicl ottoms in sewter t 34 ppt nd temperture of C. The rotifers were fed Bker`s yest (2.6 g per million rotifers dy -1 ) dissolved in sewter tht ws continuously pumped into the tnks. For long term enrichment Multigin (0.14 g per million rotifers) lended with sewter ws dded to the rotifer tnks twice dy. Deris ws removed from the tnk dily y flushing from n outlet t the ottom of the tnk for 5 seconds. Due to high mount of prticles in the wter (yest, Multigin, wstes) the rotifer tnks hd to e clened once week. The rotifers were trnsferred into holding tnk while the rotifer tnks were clened out. The tnks were filled with clen wter nd the rotifers were put ck in. The density nd egg rtio of ech culture ws estimted every morning. From wter smples tken from ech tnk 12 drops of 25 µl ws tken out nd the numer of individuls nd numer of eggs were counted in ech drop. The highest nd lowest count ws cncelled out nd the mount in the remining 10 drops ws dded together to get the egg rtio nd further multiplied to get the numer of individuls per liter. The desired mount of rotifers were then tken out from tnk nd concentrted nd wshed in 64 µm sieve. The rotifers were then put in 100 L tnk with sewter (24 C nd moderte ertion) nd were short term enriched with Multigin (0.14 g per million 8

15 individuls) for 2 hours. Before feeding them to the lrve the density ws doule checked efore the desired mount for one feeding ws tken out, wshed nd concentrted. The remining rotifers were stored cold (8 C nd under moderte ertion) to keep the nutritionl vlue stle until the following feedings Cultivtion of Artemi frnciscn Dry Artemi cysts were hydrted in fresh wter (4.9 liter of wter for g cysts, C) under hevy ertion for one hour efore eing decpsulted. The decpsultion process ws done ccording to Sorgeloss et l. (1977) g NOH dissolved in 150 ml of wter nd 1.44 L of NOCl ws dded to the hydrted cysts. The process ws stopped when the cysts chnged color from rown to ornge. The decpsulted cysts were filtered through 125 µm mesh net nd rinsed under running wter for out 5 minutes. The cysts were then concentrted nd stored t 5 C nd used within 6 dys. The desired mount of decpsulted cysts ws put in tnk with 60 L of sewter (25-28 C) with hevy ertion for 24 hours for htching. The htched Artemi ws wshed in n Artemi-wsher for 10 minutes. The wshed nuplii ws then concentrted nd trnsferred to new tnk. The Artemi ws enriched twice with Multigin (10 g/60l; Biomr) during the next 24 hours. The Artemi ws then hrvested, rinsed nd concentrted efore eing fed to the fish lrve. 2.3 Lrvl smpling nd fixtion Fish lrve were rndomly smpled from the tnks using ldle. The ldle ws rinsed with hot fresh wter etween ech smpling to void trnsferring cteri. The first smpling done on 3 dph ws done efore the lrve were trnsferred to the different tretment tnks. After this point n equl numer of individuls were smpled from ech tnk on smple dys. The collected lrve were nesthetized using tricine methnesulfonte (MS-222, Finquel, Agent Chemicl Lortories Inc., USA) nd then rinsed in distilled wter. The fish smpled for histologicl nlysis were fixted in 4 % prformldehyde (PFA) in 0.11M hepes uffer nd stored cold (4 C) in glss vils. 9

16 2.3.1 Stndrd length nd myotome height Mesurement on stndrd length (SL) nd myotome height (MH) were done on lrve collected on 6 different dys: 3, 8, 15, 28, 36 nd 45 dph. On 3 dph 20 lrve were smpled from the egg incutor efore the remining lrve were distriuted to the different tretment tnks. On the other dys lrve were smpled from ech tnk. The lrve were nesthetized nd SL nd MH were mesured from pictures y using Nikon SMZ1000 stereomicroscope nd Infinity 1-3C cmer. SL ws mesured from the tip of the mouth to the end of the notochord on smll lrve nd to the strt of the til fin on lrger lrve. MH ws mesured perpendiculr to the xil skeleton, right ehind the nus. SL nd MH mesurements were performed y Stine Wiorg Dhle (SINTEF). After imge nlysis the sme lrve were rinsed in distilled wter nd smpled for CN-nlysis Dry weight nd dily weight increse The sme lrve used for SL nd MH mesurements were used for CN-nlysis. The lrve were nlyzed for cron content y using n Elementl Comustion Anlyzer (Costech Anlyticl Technologies Inc., USA) with cetnilide s stndrd (nlysis done y Mrthe Schei, SINTEF). Lrvl dry weight ws clculted y using the eqution: DW= (µg cron lrve -1 )* 2.34 (Reitn et l., 1993) Specific growth rte (SGR) nd dily weight increse (%DWI) ws further clculted using these equtions ccording to Ricker (1958): SGR = ln W 2 lnw 1 t 2 t1 %DWI = (e SGR 1) * 100 where W 1 nd W 2 re the dry weight t time t 1 nd t Survivl From 15 dph ded fish lrve were siphoned off the ottom of the tnks nd counted every second/third dy. At the end of the experiment (45 dph) the remining fish in the tnks were counted. The dt ws corrected for smpled lrve nd the lrve tht were ccidentlly removed during clening of the tnks. The mortlity up to 15 dph ws considered to show negtive liner regression with time. 10

17 2.4 Histologicl nlysis 5 fixted lrve from 3 dph nd 5 fixted lrve from ech tretment from 6, 8 nd 15 dph were emedded in EPON (Appendix 1). Sections were mde through the liver nd the midgut (Figure 2.1) for further nlysis in light microscope (1 µm thick sections) nd in trnsmission electron microscope (70 nm thick sections) with Leic Richert Ultrcut microtome (Leic Microsystems, Germny). The 70 nm thick sections for electron microscopy were performed y Tor Brdl, NTNU. Figure 2.1: Blln wrsse lrve 8 dph showing where the liver nd gut sectioning were performed. Photo: Mren Rnheim Ggnt 11

18 2.4.1 Light microscope The sections were stined with Toluidine Blue nd Borte uffer nd studied under Zeiss Axioscope2 plus microscope (Zeiss Inc., Germny) equipped with JVC TK-C1381 color video cmer (JVC, Jpn). The sections were nlyzed with n imge processing progrm clled Imge-J. On oth the sections from the liver nd the gut the nucleus re size ws mesured using Imge J Trnsmission electron microscope The sections were contrsted with led citrte nd oserved in Jeol JEM-1011 trnsmission electron microscope (Jeol LTD, Jpn) t n ccelerting voltge t 80 kv y Tor Brdl (NTNU). The photos tken from the trnsmission electron microscope ws further nlyzed with the imge processing progrm Imge J. In Imge J point grid ws locted on rndomly selected photos (x mgnifiction) tken of the liver nd gut sections. Ech point covered given re. On the liver sections the totl re covered y mitochondri, lipid, glycogen, endoplsmic reticulum (ER), nucleus nd generl cytosol ws mesured. On the photos of the gut sections the re covered y mitochondri, ER, nucleus, generl cytosol nd vcuole 1 nd 2 ws mesured. This gve two-dimensionl quntifiction nd the re frction of the different orgnelles ws clculted. On the photos of the liver nd gut sections mitochondri size ws mesured nd qulittive study on mitochondril structure nd ppernce ws done. On the sections of the gut microvilli height nd density ws lso mesured. 2.5 Sttisticl nlysis Dt tht consisted of percentge vlues were trnsformed using n rc-sine trnsformtion efore eing sttisticlly tested. Difference of mens ws tested using one-wy ANOVA (P<0.05). An F-test were performed to check for homogeneity of vrince (p=0.05). A T-test for equl vrince ws performed if there ws homogeneity of vrince nd T-test for unequl vrince if there ws not. The sttisticl testing ws done in Microsoft Office Excel nd grphs were mde in SigmPlot 12.5 (Systd Softwre Inc., USA 2013). 12

19 3 Results 3.1 Growth nd survivl Dry weight nd dily weight increse Men dry weight (DW) of the lln wrsse lrve t the eginning of the experiment ws ± 2.07 µg. At 8 dph there ws lredy difference in DW etween the lrvl groups, nd t 15 dph the Copepod-group hd significntly higher DW of 191 ± 11 µg lrv -1 versus 82 ± 0.69 µg lrv -1 for the Rotifer-group (Figure 3.1). The difference etween the Rotifer nd the Copepod-group continued pst 28 dph (figure 3.2), ut fter 30 dph, when the Rotifergroup were wened on to Artemi sp., the difference decresed nd there ws no significnt difference etween the groups from 36 dph until the end of the experiment. Both groups hd slowdown in the increse of dry weight etween 28 nd 36 dph, with it incresing gin etween 36 nd 45 dph. For the Rotifer-group this ws the eginning of the wening period on to rtemi which could men tht they hd hrd time ccepting the new feed t first. The slowdown in dry weight increse in the Copepod-group could e due to su-optiml numers nd size of the copepods they were fed. When the feeding ws chnged from copepodits to copepodits nd 1/3 dult copepods t 36 dph the men dry weight incresed more rpidly gin. The dily weight increse (DWI) of oth lrvl groups ws negtive in the first period of the experiment prior to exogenous feeding (Figure 3.3). In the period of 8-15 dph oth groups hd positive DWI with significntly higher DWI in the Copepod-group with 18.8 ± 2.5 % versus 8.7 ± 2 % in the Rotifer-group. Over the next two time intervls, nd dph there ws decrese in DWI for the Copepod-group efore it incresed gin t dph. This cn e explined y the issue of the su-optiml feeding regime discussed erlier. When the dult copepods were introduced in the diet t 36 dph, the DWI incresed gin. The decrese in DWI in the Rotifer-group t dph cn e explined y the wening onto Artemi in this time period. After the lrve were fully wened onto rtemi the DWI incresed gin t dph, nd ws t the sme level s the Copepod-group t round 15 %. Looking t the men DWI for the whole strt feeding period (3-45 dph) there ws no significnt difference etween the groups nd it ws t 10.5 % for the Copeopod-group nd 9.25 % for the Rotifer-group. 13

20 1,00 COP ROT Men dry weigt (mg/lrv) 0,10 0, Dys post htch Figure 3.1: Men dry weight (mg lrv 1 ) of lln wrsse lrv from 3 to 15 dph were Rotifer group were fed rotifers nd Copepod-group fed copepod nuplii (y-xis presented in logrithmic scle). Dt re men ±SE (n=20-35). Letters indictes significnt difference. 10 N C C+A(2:1) Men dry weight (mg/lrv) 1 0,1 COP ROT 0, Dys post htch Figure 3. 1: Men dry weight (mg lrv -1 ) for the whole strt feeding experiment of 45 dys (y-xis presented in logrithmic scle). Letters indictes significnt difference etween the groups. Error rs indictes ± SE. The re etween the dshed lines mrks the time of co-feeding with rotifers nd rtemi (30-41 dph). The rrow heds mrks the time of feeding with copepod nuplii (N) 3-15 dph, copepodits (C) dph nd copepodits nd dult copepods (A) dph. 14

21 25 20 COP ROT c c c Men % DWI c c c c Dys post htch Figure 3.2: Dily weight increse (DWI, %) for the lln wrsse lrve during the whole strt-feeding experiment consisting of 45 dys split into five intervls nd one for the whole experiment. Letters indictes significnt difference etween tretments nd within tretments. Error rs indicte ± SE. 15

22 3.1.2 Stndrd length (SL) nd myotome height (MH) In the eginning of the experiment from 3 to 8 dph there ws negligile increse in SL in oth lrvl groups, nd no significnt difference etween the groups, 3.93±0.07 for the Copepod-group nd 3.87±0.02 for the Rotifer-group (Figure 3.4). From 15 dph nd throughout the experiment the Copepod-group hd significntly higher SL thn the Rotifergroup. The myotome height of the Copepod lrve ws significntly higher thn tht of the lrve from the Rotifer-group t 8 dph nd throughout the whole experiment (Figure 3.5). The Rotifer-group didn t hve significnt increse in myotome height efore 28 dph. 14 Men stndrd lenght (mm) dph COP ROT Dys post htch Figure 3.3: Mesured stndrd lenght (SL) t 3 dph, 8 dph, 15 dph, 28 dph, 36 dph nd 45 dph (n=12 for 3 nd 8 dph, n=20 for 15, 28, 36 nd 45 dph). Letters indictes significnt difference etween tretments. Error rs indicte ± SE. 16

23 Men myotome height (mm) 3,0 2,5 2,0 1,5 1,0 0,5 3 dph COP ROT 0, Dys post htch Figure 3.4: Mesured myotome height (MH) t 3 dph, 8 dph, 15 dph, 28 dph, 36 dph nd 45 dph (n=12 for 3 nd 8 dph, n=20 for 15, 28, 36 nd 45 dph). Letters indicte significnt differences etween tretments. Error rs indictes ± SE Survivl The highest mortlity ws t the eginning of the first feeding experiment. From 15 dph nd throughout the experiment there ws no significnt difference in % survivl etween the two groups. At 45 dph when the experiment ws terminted, the Copepod-group hd slightly higher survivl thn the Rotifer-group, ut the difference ws not significnt. Tle 3.1: Men survivl (%) ± SE of ech tretment t 15, 22, 29, 37 nd 45 dph (n=3). No significnt difference ws found etween the two tretments Men survivl (%) ± SE DPH ROT COP ±1 15 ± ±0 13 ± ±1 12 ± ±1 12 ± ±1 11 ±2 17

24 3.2 Liver morphology Light microscopy The liver tissue in the lrve t 3 dph seemed quite undeveloped with irregulrly shped nuclei without clerly defined nucleoli. In ll of the lrve tested there ws residue of yolk nd syncytium round the liver tissue, nd in two of the lrve tested liver tissue ws not found t ll. At 8 dph the liver tissue ws more developed nd orgnized s loules with visile lood vessels nd lood cells (Figure 3.6 B-C). The nuclei hd rounder shpe with clerly defined nucleoli. The liver in the Rotifer-group t 8 dph seemed less developed with less liver tissue compred to the Copepod-group. At 15 dph the liver tissue in oth groups ws more developed compred to the erlier smple dtes. The liver ws lrger in volume with visile lood vessels nd glycogen deposits throughout the tissue (Figure 3.6 D-E). Figure 3.6 A: Photo microgrph of the liver t 3 dph. The tissue is undeveloped with no visile lood vessels nd irregulrly shped nuclei without defined nucleoli. 18

25 Figure 3.6 B: Photo microgrph of the liver of lrve t 8 dph from the Rotifer-group. The liver is orgnized into loules ut the tissue seems more immture thn the liver tissue in the Copepod-group. The nuclei re rounder in shpe nd hve defined nucleoli. Figure 3.6 C: Photo microgrph of the liver of lrve t 8 dph from the Copepod-group. The tissue seems more developed nd orgnized thn t 3 dph nd compred to the liver tissue from the Rotifer-group. There re visile lood vessels nd lood cells. The nuclei re rounder in shpe with defined nucleoli. 19

26 Figure 3.6 D: Photo microgrph of the liver of lrve t 15 dph from the Rotifer-group. The tissue is more developed thn t the erlier smple dtes. There re visile lood vessels nd lood cells, nd visile glycogen deposits. Figure 3.6 E: Photo microgrph of the liver of lrve t 15 dph from the Copepod-group. The tissue is more developed with visile lood vessels. Glycogen deposits re lso visile throughout the tissue. 20

27 3.2.2 Trnsmission electron microscopy The heptocytes were seen s polygonl cells with lrge, sphericl nuclei (Figure 3.7). Visile orgnelles consisted of nuclei, mny mitochondri nd rough endoplsmic reticulum (ER) which were more defined t 15 dph thn t 3 dph. Glycogen ws oserved in the liver lredy t 3 dph, lthough t low mounts. The mount of glycogen in the liver grdully incresed over time nd ws most undnt in the Rotifer-group t 15 dph (Figure 3.7 D). In the lrve from the Rotifer-group t 15 dph the glycogen ws scttered throughout the cells while in the lrve from the Copepod-group the glycogen ws more clustered together. At 3 nd 8 dph the mitochondril memrnes ws generlly more rugged thn t 15 dph with not much difference etween the groups t 8 dph. At 15 dph the Copepod-group hd lrger proportion of smooth outer mitochondril memrnes thn the Rotifer-group. At 3 dph there were much lrger proportion of mitochondri with less dense criste thn t 8 nd 15 dph (Figure 3.7 A). At 15 dph the ER ws much more undnt nd orgnized thn on 3 nd 8 dph nd is seen enveloping the mitochondri (Figure 3.7 D-E). Figure 3.7 A: Microgrph tht shows the generl morphology of liver tissue from lrve t 3 dph. Nuclei (N) nd mitochondri (M) re shown on the photos. The photos show difference in mitochondril ppernce, undnce nd orgniztion of ER nd occurrence of glycogen over time. Mitochondri memrnes re more rugged (rrow) nd criste less dense (str) t 3 dph thn t the lter smple dtes. Endoplsmic reticulum is more undnt nd orgnized t 15 dph nd glycogen ws seen in oth groups from 8 dph. 21

28 Figure 3.7 B: Microgrph tht shows the generl morphology of liver tissue from lrve from the Rotifer tretment t 8 dph. Mitochondri (M) nd ile ducts (BD) re shown on the photos. Rugged memrnes mrked with rrows. Figure 3.7 C: Microgrph tht shows the generl morphology of liver tissue from lrve from the Copepod tretment t 8 dph. Nuclei (N), mitochondri (M) nd glycogen (G) nd endoplsmic reticulum (ER) re shown on the photos. Rugged memrne mrked with rrow. 22

29 Figure 3.7 D: Microgrph tht shows the generl morphology of liver tissue from lrve from the Rotifer tretment t 15 dph. Nuclei (N), mitochondri (M), glycogen (G) nd endoplsmic reticulum (ER) re shown on the photos. Figure 3.7 E: Microgrph tht shows the generl morphology of liver tissue from lrve from the Copepod tretment t 15 dph. Nuclei (N), mitochondri (M), glycogen (G) nd endoplsmic reticulum (ER) re shown on the photos. 23

30 3.2.3 Surfce re frction of heptocyte components Glycogen ws found in the liver lredy t 3 dph, lthough in low levels, 1.2 ± 0.4 %. The surfce re frction of glycogen incresed over time in oth groups nd the highest frction ws found in the Rotifer-group t 15 dph with 38.3 ± 3 % (Figure 3.7). There ws no significnt difference in the surfce re frction of mitochondri etween or within the two tretments over time. The surfce re frction of the nuclei decresed over time for oth tretments nd the nucleus re frction on 3 dph ws significntly higher thn the nucleus re frction t 15 dph. 100 Men surfce re frction(%) c D2 D8 ROT D8 COP D15 ROT D15 COP c c Nucleus Mitochondri Glycogen Other c c Tretment Figure 3.8: Men surfce re frction (%) of heptocyte cell components (nuclei, mitochondri, nd glycogen) on 3 dph, 8 dph nd 15 dph for oth tretments (n=5). Letters indictes significnt difference etween nd within tretments. Error rs indictes ± SE. 24

31 3.2.4 Are size of nucleus nd mitochondri The nucleus re size ws the smllest t 3 dph (91.2 ± 2.2 µm 2 ), ut it is not significntly smller thn the nucleus size in either group t 8 dph (Figure 3.9 A). There ws slight increse in nucleus re size over time ut only significntly for the Copepod-group t 15 dph (118.6 ± 2.6 µm 2 ). The mitochondri were the smllest t 3 dph (0.74 ± 0.07 µm 2 ), nd there ws significnt increse in mitochondri size from 3 dph to 8 dph for oth groups (Figure 3.9 B). The mitochondri size for the Rotifer-group ws significntly higher thn the Copepod-group on 8 dph nd oth groups on 15 dph (2.85 ± 0.9 µm 2 ), ut the high stndrd error indictes gret vrition in the smple. At 15 dph there ws no difference in mitochondri size etween the groups, with size of round 2 ± 0.3 µm 2 for oth groups. Nucleus re size( m 2 ) A Mitochondri size( m 2 ) B c c c dph D8COP D8ROT D15COPD15ROT 0 3 dph D8 ROT D8 COP D15 ROT D15 COP Tretment Tretment Figure 3.9: Nucleus re size (A) nd mitochondri size (B) in the heptocytes of lrve from 3 dph nd from oth tretments t 8 nd 15 dph. Letters indictes significnt difference etween nd within the groups. Error rs indictes ± SE. 25

32 3.2.5 Mitochondril chrcteristics Over time there is n overll decrese in the occurrence of rugged outer mitochondril memrnes. At 3 dph most of the mitochondri hd rugged outer memrne (96.6 ± 3 %). At 8 dph the proportion of smooth outer memrne hd incresed ut still the mjority hd rugged ppernce. At 15 dph there ws significnt difference etween the two groups, where the Copepod-group hd igger proportion of smooth outer memrnes thn the Rotifer-group. Outer mitochondril memrne ppernce (%) Tretment 3 dph 8 dph ROT 8 dph COP 15 dph ROT 15 dph COP c Smooth Rugged Figure 3.10: Men outer mitochondril memrne ppernce (%) in the liver of lrve t 3 dph nd from oth tretments t 8 nd 15 dph (n=5). The outer mitochondril memrne is clssified s either smooth or rugged. There ws significntly higher occurrence of rugged memrne structure t 3 dph thn t the lter smple dys nd the highest occurrence of smooth memrne structure ws found on 15 dph in the Copepod-group. Letters indictes significnt difference etween nd within tretments. Error rs indictes ± ER. 26

33 Over time there ws significnt decrese in the occurrence of less dense criste nd significnt increse in the occurrence of denser criste. At 8 dph oth groups hd significnt increse in the occurrence of denser criste when compred to 3 dph, where the Rotifer-group significntly higher proportion of denser criste thn the Copepod-group. At 15 dph oth groups hd high proportion of dense criste where the Copepod-group hd significntly higher proportion thn the Rotifer-group. Interdigitted criste were found in individuls from the Rotifer-group oth t 8 nd 15 dph with the highest occurrence t 15 dph (14 ± 4 %). 100 d Men criste ppernce (%) c * Less dense Denser Interdigitted 0 3 dph 8 dph ROT8 dph COP15 dph ROT15 dph COP Tretment Figure 3.11: Men criste ppernce (%) in heptocytes of lrve from 3 dph nd from oth tretments t 8 nd 15 dph (n=5). There ws significnt difference etween the tretments t oth 8 nd 15 dph nd significntly less dense criste t 3 dph. Interdigitted criste ws mostly found in the Rotifer-tretment with the highest occurrence t 15 dph (*). Letters indictes significnt difference etween nd within tretments. Error rs indictes ± SE. 27

34 3.3 Gut morphology Light microscopy At 3 dph the digestive trct ws short nd nrrow with thick intestinl epithelium. The enterocytes were long nd nrrow nd the nuclei were olong in shpe with no distinguishle nucleoli (Figure 3.12 A). At 8 dph the digestive trct ws wider thn t 3 dph nd the enterocytes were more distinguishle s columnr cells with round nuclei (Figure 3.12 B-C). The intestinl epithelium in the Copepod-group ws strting to fold more thn the epithelium in the Rotifer-group. Two of the lrve from the Rotifer-group t 8 dph hd thinner intestinl epithelium with less dense (Figure 3.19) nd shorter microvilli (Figure 3.18), exhiiting signs of strvtion. At 15 dph the epithelium ws thicker nd hd more folds thn t 8 dph for oth groups. The microvilli order on the luminl surfce ws longer in the Copepod-group thn the Rotifer-group t 15 dph nd oth groups t 8 dph (Figure 3 18). At the se of the enterocytes in the Rotifer lrve from 15 dph (Figure 3.12 D) numerous lipid droplets were visile. Lipid droplets were lso seen in the enterocytes of the Copepod-group ut they were more dispersed throughout the cells nd not s numerous. Figure 3.12 A: Photo microgrph of the midgut of lrv t 3 dph. The digestive trct is nrrow with thick intestinl epithelium. Visile microvilli order towrds the digestive trct. The enterocytes nd nuclei re long nd nrrow. 28

35 Figure 3.12 B: Photo microgrph of the midgut of lrv t 8 dph from the Rotifer-group. The digestive trct is wider nd the intestinl epithelium is nrrower thn t 3 dph. The cells re more qudrtic in shpe nd the nuclei hve ecome more round. Visile microvilli order towrds the digestive trct. Figure 3.12 C: Photo microgrph of the midgut of lrv t 8 dph from the Copepod-group. The digestive trct is wider thn on 3 dph. The epithelium is more folded thn in the Rotifer-group. Here the nuclei re lso more round thn t 3 dph. Visile microvilli order towrds the digestive trct. 29

36 Figure 3.12 D: Photo microgrph of the midgut of lrv t 15 dph from the Rotifer-group. The intestinl epithelium is thicker nd more folded thn on erlier smple dtes. Numerous lipid droplets re visile t the se of the enterocytes.. Figure 3.12 E: Photo microgrph of the midgut of lrv t 15 dph from the Copepod-group. The intestinl tissue is thicker nd more folded thn on erlier smple dtes. The microvilli order is thicker nd longer thn in the Rotifer group.. 30

37 3.3.2 Trnsmission electron microscopy The intestinl epithelium of the lrve consisted of tll columnr enterocytes with the nuclei t the se of the cells nd order of microvilli t the top. Visile orgnelles were nuclei, mitochondri nd endoplsmic reticulum (ER). The outer mitochondril memrnes were more rugged t 3 dph thn t lter smple dtes (Figure 3.13 A). At 8 dph oth groups hve lrger proportion of rugged thn smooth memrnes ut less so thn t 3 dph. At 15 dph oth groups hve smoother outer mitochondri memrnes with no ig difference etween the groups. There ws no ig difference in criste density over time either within or etween groups, though more incidents of less dense criste t 3 dph thn t lter smple dtes (Figure 3.13 A). At 15 dph the ER ws much more undnt nd orgnized in the enterocytes of the Copepod-group thn for the Rotifer-group nd oth of the groups t 8 dph (Figure 3.13 E). Two unidentified vcuoles were oserved in the enterocytes of the Rotifer-group t 8 nd 15 dph. Vcuole 1 ws round with white droplets inside (Figure 3.13 B), while vcuole 2 hd grey color with drker outer ring. 31

38 Figure 3.13 A: Microgrph tht shows the generl morphology of intestinl tissue in the midgut from lrve t 3 dph. Nuclei (N), mitochondri (M) nd microvilli (MV) re shown on the photos. The photos show difference in mitochondril memrne structure nd criste density over time nd endoplsmic reticulum gets more undnt nd orgnized over time. At 3 dph the outer mitochondril memrnes re more rugged (rrow) nd the criste less dense (*) thn t 15 dph. 32

39 Figure 3.13 B: Microgrph tht shows the generl morphology of intestinl tissue in the midgut from lrve from the Rotifer-tretment t 8 dph. Nuclei (N), mitochondri (M), vcuole 1 (V1) nd microvilli (MV) re shown on the photo. The rrow mrks mitochondri with rugged outer memrne. Figure 3.13 C: Microgrph tht shows the generl morphology of intestinl tissue in the midgut from lrve from the Copepod-tretment t 8 dph. Nuclei (N) nd mitochondri (M) re shown on the photo. 33

40 Figure 3.13 D: Microgrph tht shows the generl morphology of intestinl tissue in the midgut from lrve from the Rotifer-tretment t 15 dph. Nuclei (N), mitochondri (M) re shown on the photo. Figure 3.13 E: Microgrph tht shows the generl morphology of intestinl tissue in the midgut from lrve from the Copepod-tretment t 15 dph. Mitochondri (M) nd endoplsmic reticulum (ER) re shown on the photo. 34

41 3.3.3 Surfce re frctions of enterocyte components The surfce re frction of nuclei ws highest t 3 dph (20.6 ± 2.3 %) nd decresed slightly over time for oth groups ut there ws no significnt difference etween or within tretments (Figure 3.14). The surfce re frction of mitochondri decresed slightly over time nd there ws significnt difference etween 3 dph nd oth tretments on 8 nd 15 dph (Figure 3.14). The surfce re frction of endoplsmic reticulum (ER) in the enterocytes of the Rotifergroup decreses slightly from 3 to 8 dph ut then seems to stilize t round 25 %. In the Copepod-group there lso is decrese in the ER re frction from 3 to 8 dph, ut t 15 dph there is significnt increse in the frction of ER from 23.5 to 34.2 %. Vcuole 1 nd vcuole 2 ws unidentified vcuoles nd were only found in individuls from the Rotifer tretment t 8 nd 15 dph. The highest vlue of vcuole re frction ws found on 8 dph for vcuole 1 (8.4 ± 1 %), which ws significntly higher thn on 15 dph (3.6 ± 1 %). The surfce re frction of vcuole 2 hd slight increse from 8 to 15 dph ut the difference ws not significnt. 100 Men re frction (%) c Nucleus Mitochondri ER Cytosol Vcuole type 1 Vcuole type 2 c 0 D2 D8 ROT D8 COP D15 ROT D15 COP Tretment Figure 3.14: Men surfce re frction (%) of enterocyte cell components (nuclei, mitochondri, endoplsmic reticulum (ER), generl cytosol, vcuole 1 nd 2 nd microvilli) on 3 dph, nd for oth tretments t 8 dph nd 15 dph (n=5). Letters indictes significnt difference etween nd within tretments. Error rs indictes ± SE. 35

42 3.3.4 Are size of nucleus nd mitochondri There ws n overll increse in nucleus re size over time for oth groups. The smllest nucleus re size ws found in the Rotifer-group (89.2 ± 2 µm 2 ) t 8 dph which ws ctully smller thn t 3 dph (102.6 ± 3.4 µm 2 ). The lrgest nucleus re size ws found in the Copepod-group t 15 dph (137.8 ± 3.2 µm 2 ) which ws significntly lrger thn the nuclei t 3 dph nd the nucleus re size in the Rotifer group t 8 dph. The generl trend for mitochondril re size for oth groups ws decrese in size over time ut there ws no significnt difference etween the groups or etween the groups nd 3 dph. The lrgest mitochondril re size ws t 8 dph in the Rotifer-group (1 ± 0.08 µm 2 ) nd the smllest in the Rotifer-group t 15 dph (0.73 ± 0.06 µm 2 ) A c c c 1,2 1,0 B Nucleus Are size( m 2 ) Mitochondril re size ( m 2 ) 0,8 0,6 0,4 20 0,2 0 D3 D8 Rot D8 Cop D15 Rot D15 Cop 0,0 D3 D8 Rot D8 Cop D15 Rot D15 Cop Tretments Tretment Figure 3.15: Nucleus re size (A) nd mitochondri size (B) in the enterocytes of lrve from 3 dph nd from oth tretments t 8 nd 15 dph. Letters indictes significnt difference etween nd within the groups. No significnt difference in mitochondri size ws found. Error rs indictes ± SE. 36

43 3.3.5 Mitochondril ppernce The highest occurrence of rugged outer mitochondril memrnes ws seen t 3 dph nd there seemed to e generl decrese in the occurrence of rugged memrnes over time for oth groups. At 15 dph the lrve from the Copepod-group seemed to hve more mitochondri with smooth outer memrnes thn the lrve from the Rotifer-group, ut the difference etween the groups were negligile. 100 Mitochondril memrne ppernce (%) c c c Smooth Rugged 0 3 dph 8 dph ROT 8 dph COP 15 dph ROT 15 dph COP Tretment Figure 3.16: Men outer mitochondril memrne ppernce (%) in the enterocytes of lrve t 3 dph nd from oth tretments t 8 nd 15 dph (n=5). There ws significntly higher occurrence of rugged memrne structure t 3 dph thn t the lter smple dys nd the highest occurrence of smooth memrne structure ws found on 15 dph in the Copepod-group. Letters indictes significnt difference etween nd within tretments. Error rs indictes ± ER. 37

7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus

7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus 7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e

More information

Section 6: Area, Volume, and Average Value

Section 6: Area, Volume, and Average Value Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find

More information

THE EFFECT OF GRADED DIETARY LEVELS OF VITAMIN A, GIVEN TO EARLY SEA BREAM (Sparus aurata) LARVAE ON SKELETAL DEFORMITIES AND GENOMIC EXPRESSION

THE EFFECT OF GRADED DIETARY LEVELS OF VITAMIN A, GIVEN TO EARLY SEA BREAM (Sparus aurata) LARVAE ON SKELETAL DEFORMITIES AND GENOMIC EXPRESSION THE EFFECT OF GRADED DIETARY LEVELS OF VITAMIN A, GIVEN TO EARLY SEA BREAM (Sprus urt) LARVAE ON SKELETAL DEFORMITIES AND GENOMIC EXPRESSION B. Ginzourg, W.M. Koven, S. Fontgne, A. Sgi, D. M. Power nd

More information

Interpreting Integrals and the Fundamental Theorem

Interpreting Integrals and the Fundamental Theorem Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of

More information

Discrete Mathematics and Probability Theory Spring 2013 Anant Sahai Lecture 17

Discrete Mathematics and Probability Theory Spring 2013 Anant Sahai Lecture 17 EECS 70 Discrete Mthemtics nd Proility Theory Spring 2013 Annt Shi Lecture 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion,

More information

Discrete Mathematics and Probability Theory Summer 2014 James Cook Note 17

Discrete Mathematics and Probability Theory Summer 2014 James Cook Note 17 CS 70 Discrete Mthemtics nd Proility Theory Summer 2014 Jmes Cook Note 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion, y tking

More information

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of

More information

The 1 th International and The 4 th National Congress on Recycling of Organic Waste in Agriculture April 2012 in Isfahan, Iran

The 1 th International and The 4 th National Congress on Recycling of Organic Waste in Agriculture April 2012 in Isfahan, Iran The 1 th Interntionl nd The 4 th Ntionl Congress on The Effect of Prticle Size nd Composting Period on (C/N) Rtio of Dte- Plm Wste Min Mortzvi 1, Ahmd Mohmmdi Ghehsreh 2 nd Mhmoud Klsi 3 1. M.Sc. Student,

More information

2.4 Linear Inequalities and Interval Notation

2.4 Linear Inequalities and Interval Notation .4 Liner Inequlities nd Intervl Nottion We wnt to solve equtions tht hve n inequlity symol insted of n equl sign. There re four inequlity symols tht we will look t: Less thn , Less thn or

More information

p-adic Egyptian Fractions

p-adic Egyptian Fractions p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction

More information

( ) as a fraction. Determine location of the highest

( ) as a fraction. Determine location of the highest AB Clculus Exm Review Sheet - Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if

More information

( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).

( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x). AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f

More information

Chapters Five Notes SN AA U1C5

Chapters Five Notes SN AA U1C5 Chpters Five Notes SN AA U1C5 Nme Period Section 5-: Fctoring Qudrtic Epressions When you took lger, you lerned tht the first thing involved in fctoring is to mke sure to fctor out ny numers or vriles

More information

2 b. , a. area is S= 2π xds. Again, understand where these formulas came from (pages ).

2 b. , a. area is S= 2π xds. Again, understand where these formulas came from (pages ). AP Clculus BC Review Chpter 8 Prt nd Chpter 9 Things to Know nd Be Ale to Do Know everything from the first prt of Chpter 8 Given n integrnd figure out how to ntidifferentite it using ny of the following

More information

Linear Systems with Constant Coefficients

Linear Systems with Constant Coefficients Liner Systems with Constnt Coefficients 4-3-05 Here is system of n differentil equtions in n unknowns: x x + + n x n, x x + + n x n, x n n x + + nn x n This is constnt coefficient liner homogeneous system

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

AB Calculus Review Sheet

AB Calculus Review Sheet AB Clculus Review Sheet Legend: A Preclculus, B Limits, C Differentil Clculus, D Applictions of Differentil Clculus, E Integrl Clculus, F Applictions of Integrl Clculus, G Prticle Motion nd Rtes This is

More information

Physics 1402: Lecture 7 Today s Agenda

Physics 1402: Lecture 7 Today s Agenda 1 Physics 1402: Lecture 7 Tody s gend nnouncements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW ssignments, solutions etc. Homework #2: On Msterphysics tody: due Fridy Go to msteringphysics.com Ls:

More information

Applications of Bernoulli s theorem. Lecture - 7

Applications of Bernoulli s theorem. Lecture - 7 Applictions of Bernoulli s theorem Lecture - 7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.

More information

Review of Gaussian Quadrature method

Review of Gaussian Quadrature method Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge

More information

Note 12. Introduction to Digital Control Systems

Note 12. Introduction to Digital Control Systems Note Introduction to Digitl Control Systems Deprtment of Mechnicl Engineering, University Of Ssktchewn, 57 Cmpus Drive, Ssktoon, SK S7N 5A9, Cnd . Introduction A digitl control system is one in which the

More information

( ) Same as above but m = f x = f x - symmetric to y-axis. find where f ( x) Relative: Find where f ( x) x a + lim exists ( lim f exists.

( ) Same as above but m = f x = f x - symmetric to y-axis. find where f ( x) Relative: Find where f ( x) x a + lim exists ( lim f exists. AP Clculus Finl Review Sheet solutions When you see the words This is wht you think of doing Find the zeros Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor Find

More information

Continuous Random Variable X:

Continuous Random Variable X: Continuous Rndom Vrile : The continuous rndom vrile hs its vlues in n intervl, nd it hs proility distriution unction or proility density unction p.d. stisies:, 0 & d Which does men tht the totl re under

More information

Ch AP Problems

Ch AP Problems Ch. 7.-7. AP Prolems. Willy nd his friends decided to rce ech other one fternoon. Willy volunteered to rce first. His position is descried y the function f(t). Joe, his friend from school, rced ginst him,

More information

Student Activity 3: Single Factor ANOVA

Student Activity 3: Single Factor ANOVA MATH 40 Student Activity 3: Single Fctor ANOVA Some Bsic Concepts In designed experiment, two or more tretments, or combintions of tretments, is pplied to experimentl units The number of tretments, whether

More information

Math 8 Winter 2015 Applications of Integration

Math 8 Winter 2015 Applications of Integration Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl

More information

10. AREAS BETWEEN CURVES

10. AREAS BETWEEN CURVES . AREAS BETWEEN CURVES.. Ares etween curves So res ove the x-xis re positive nd res elow re negtive, right? Wrong! We lied! Well, when you first lern out integrtion it s convenient fiction tht s true in

More information

SUMMER KNOWHOW STUDY AND LEARNING CENTRE

SUMMER KNOWHOW STUDY AND LEARNING CENTRE SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18

More information

The Fundamental Theorem of Calculus, Particle Motion, and Average Value

The Fundamental Theorem of Calculus, Particle Motion, and Average Value The Fundmentl Theorem of Clculus, Prticle Motion, nd Averge Vlue b Three Things to Alwys Keep In Mind: (1) v( dt p( b) p( ), where v( represents the velocity nd p( represents the position. b (2) v ( dt

More information

Reading from Young & Freedman: For this topic, read the introduction to chapter 24 and sections 24.1 to 24.5.

Reading from Young & Freedman: For this topic, read the introduction to chapter 24 and sections 24.1 to 24.5. PHY1 Electricity Topic 5 (Lectures 7 & 8) pcitors nd Dielectrics In this topic, we will cover: 1) pcitors nd pcitnce ) omintions of pcitors Series nd Prllel 3) The energy stored in cpcitor 4) Dielectrics

More information

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3 2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is

More information

This chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2

This chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2 1 Direct vrition 2 Inverse vrition This chpter will show you how to solve prolems where two vriles re connected y reltionship tht vries in direct or inverse proportion Direct proportion Inverse proportion

More information

10 Vector Integral Calculus

10 Vector Integral Calculus Vector Integrl lculus Vector integrl clculus extends integrls s known from clculus to integrls over curves ("line integrls"), surfces ("surfce integrls") nd solids ("volume integrls"). These integrls hve

More information

AQA Chemistry Paper 2

AQA Chemistry Paper 2 AQA hemistry Pper 2 1.1 A student is plnning n investigtion into how the concentrtion of hydrochloric cid ffects the rte of the rection with mrle chips. Wht is the independent vrile? Tick one ox. (1 mrk)

More information

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique? XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk out solving systems of liner equtions. These re prolems tht give couple of equtions with couple of unknowns, like: 6= x + x 7=

More information

The steps of the hypothesis test

The steps of the hypothesis test ttisticl Methods I (EXT 7005) Pge 78 Mosquito species Time of dy A B C Mid morning 0.0088 5.4900 5.5000 Mid Afternoon.3400 0.0300 0.8700 Dusk 0.600 5.400 3.000 The Chi squre test sttistic is the sum of

More information

CHAPTER 20: Second Law of Thermodynamics

CHAPTER 20: Second Law of Thermodynamics CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het

More information

Monte Carlo method in solving numerical integration and differential equation

Monte Carlo method in solving numerical integration and differential equation Monte Crlo method in solving numericl integrtion nd differentil eqution Ye Jin Chemistry Deprtment Duke University yj66@duke.edu Abstrct: Monte Crlo method is commonly used in rel physics problem. The

More information

Bridging the gap: GCSE AS Level

Bridging the gap: GCSE AS Level Bridging the gp: GCSE AS Level CONTENTS Chpter Removing rckets pge Chpter Liner equtions Chpter Simultneous equtions 8 Chpter Fctors 0 Chpter Chnge the suject of the formul Chpter 6 Solving qudrtic equtions

More information

Section 6.1 Definite Integral

Section 6.1 Definite Integral Section 6.1 Definite Integrl Suppose we wnt to find the re of region tht is not so nicely shped. For exmple, consider the function shown elow. The re elow the curve nd ove the x xis cnnot e determined

More information

Continuous Random Variables

Continuous Random Variables CPSC 53 Systems Modeling nd Simultion Continuous Rndom Vriles Dr. Anirn Mhnti Deprtment of Computer Science University of Clgry mhnti@cpsc.uclgry.c Definitions A rndom vrile is sid to e continuous if there

More information

STEP FUNCTIONS, DELTA FUNCTIONS, AND THE VARIATION OF PARAMETERS FORMULA. 0 if t < 0, 1 if t > 0.

STEP FUNCTIONS, DELTA FUNCTIONS, AND THE VARIATION OF PARAMETERS FORMULA. 0 if t < 0, 1 if t > 0. STEP FUNCTIONS, DELTA FUNCTIONS, AND THE VARIATION OF PARAMETERS FORMULA STEPHEN SCHECTER. The unit step function nd piecewise continuous functions The Heviside unit step function u(t) is given by if t

More information

Suppose we want to find the area under the parabola and above the x axis, between the lines x = 2 and x = -2.

Suppose we want to find the area under the parabola and above the x axis, between the lines x = 2 and x = -2. Mth 43 Section 6. Section 6.: Definite Integrl Suppose we wnt to find the re of region tht is not so nicely shped. For exmple, consider the function shown elow. The re elow the curve nd ove the x xis cnnot

More information

Designing Information Devices and Systems I Spring 2018 Homework 7

Designing Information Devices and Systems I Spring 2018 Homework 7 EECS 16A Designing Informtion Devices nd Systems I Spring 2018 omework 7 This homework is due Mrch 12, 2018, t 23:59. Self-grdes re due Mrch 15, 2018, t 23:59. Sumission Formt Your homework sumission should

More information

Algebra Readiness PLACEMENT 1 Fraction Basics 2 Percent Basics 3. Algebra Basics 9. CRS Algebra 1

Algebra Readiness PLACEMENT 1 Fraction Basics 2 Percent Basics 3. Algebra Basics 9. CRS Algebra 1 Algebr Rediness PLACEMENT Frction Bsics Percent Bsics Algebr Bsics CRS Algebr CRS - Algebr Comprehensive Pre-Post Assessment CRS - Algebr Comprehensive Midterm Assessment Algebr Bsics CRS - Algebr Quik-Piks

More information

Examples Using both 2-D sections from Figure 3, data has been modeled for (acoustic) P and (elastic) S wave field

Examples Using both 2-D sections from Figure 3, data has been modeled for (acoustic) P and (elastic) S wave field Suslt illumintion studies through longitudinl nd trnsversl wve propgtion Riz Ali *, Jn Thorecke nd Eric Verschuur, Delft University of Technology, The Netherlnds Copyright 2007, SBGf - Sociedde Brsileir

More information

Farey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University

Farey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University U.U.D.M. Project Report 07:4 Frey Frctions Rickrd Fernström Exmensrete i mtemtik, 5 hp Hledre: Andres Strömergsson Exmintor: Jörgen Östensson Juni 07 Deprtment of Mthemtics Uppsl University Frey Frctions

More information

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz

More information

FORM FIVE ADDITIONAL MATHEMATIC NOTE. ar 3 = (1) ar 5 = = (2) (2) (1) a = T 8 = 81

FORM FIVE ADDITIONAL MATHEMATIC NOTE. ar 3 = (1) ar 5 = = (2) (2) (1) a = T 8 = 81 FORM FIVE ADDITIONAL MATHEMATIC NOTE CHAPTER : PROGRESSION Arithmetic Progression T n = + (n ) d S n = n [ + (n )d] = n [ + Tn ] S = T = T = S S Emple : The th term of n A.P. is 86 nd the sum of the first

More information

1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 1 PYTHAGORAS THEOREM 1 1 Pythgors Theorem In this setion we will present geometri proof of the fmous theorem of Pythgors. Given right ngled tringle, the squre of the hypotenuse is equl to the sum of the

More information

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:

More information

BME 207 Introduction to Biomechanics Spring 2018

BME 207 Introduction to Biomechanics Spring 2018 April 6, 28 UNIVERSITY O RHODE ISAND Deprtment of Electricl, Computer nd Biomedicl Engineering BME 27 Introduction to Biomechnics Spring 28 Homework 8 Prolem 14.6 in the textook. In ddition to prts -e,

More information

Scientific notation is a way of expressing really big numbers or really small numbers.

Scientific notation is a way of expressing really big numbers or really small numbers. Scientific Nottion (Stndrd form) Scientific nottion is wy of expressing relly big numbers or relly smll numbers. It is most often used in scientific clcultions where the nlysis must be very precise. Scientific

More information

Temperature influence compensation in microbolometer detector for image quality enhancement

Temperature influence compensation in microbolometer detector for image quality enhancement .26/qirt.26.68 Temperture influence compenstion in microolometer detector for imge qulity enhncement More info out this rticle: http://www.ndt.net/?id=2647 Astrct y M. Krupiński*, T. Sosnowski*, H. Mdur*

More information

7.1 Integral as Net Change Calculus. What is the total distance traveled? What is the total displacement?

7.1 Integral as Net Change Calculus. What is the total distance traveled? What is the total displacement? 7.1 Integrl s Net Chnge Clculus 7.1 INTEGRAL AS NET CHANGE Distnce versus Displcement We hve lredy seen how the position of n oject cn e found y finding the integrl of the velocity function. The chnge

More information

Exam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B

Exam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B PHY 249, Fll 216 Exm 1 Solutions nswer 1 is correct for ll problems. 1. Two uniformly chrged spheres, nd B, re plced t lrge distnce from ech other, with their centers on the x xis. The chrge on sphere

More information

Section 4: Integration ECO4112F 2011

Section 4: Integration ECO4112F 2011 Reding: Ching Chpter Section : Integrtion ECOF Note: These notes do not fully cover the mteril in Ching, ut re ment to supplement your reding in Ching. Thus fr the optimistion you hve covered hs een sttic

More information

Bases for Vector Spaces

Bases for Vector Spaces Bses for Vector Spces 2-26-25 A set is independent if, roughly speking, there is no redundncy in the set: You cn t uild ny vector in the set s liner comintion of the others A set spns if you cn uild everything

More information

Chapter 9 Definite Integrals

Chapter 9 Definite Integrals Chpter 9 Definite Integrls In the previous chpter we found how to tke n ntiderivtive nd investigted the indefinite integrl. In this chpter the connection etween ntiderivtives nd definite integrls is estlished

More information

Exponents and Logarithms Exam Questions

Exponents and Logarithms Exam Questions Eponents nd Logrithms Em Questions Nme: ANSWERS Multiple Choice 1. If 4, then is equl to:. 5 b. 8 c. 16 d.. Identify the vlue of the -intercept of the function ln y.. -1 b. 0 c. d.. Which eqution is represented

More information

Minnesota State University, Mankato 44 th Annual High School Mathematics Contest April 12, 2017

Minnesota State University, Mankato 44 th Annual High School Mathematics Contest April 12, 2017 Minnesot Stte University, Mnkto 44 th Annul High School Mthemtics Contest April, 07. A 5 ft. ldder is plced ginst verticl wll of uilding. The foot of the ldder rests on the floor nd is 7 ft. from the wll.

More information

332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006

332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006 2:221 Principles of Electricl Engineering I Fll 2006 Nme of the student nd ID numer: Hourly Exm 2 Novemer 6, 2006 This is closed-ook closed-notes exm. Do ll your work on these sheets. If more spce is required,

More information

Goals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite

Goals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite Unit #8 : The Integrl Gols: Determine how to clculte the re described by function. Define the definite integrl. Eplore the reltionship between the definite integrl nd re. Eplore wys to estimte the definite

More information

0.1 THE REAL NUMBER LINE AND ORDER

0.1 THE REAL NUMBER LINE AND ORDER 6000_000.qd //0 :6 AM Pge 0-0- CHAPTER 0 A Preclculus Review 0. THE REAL NUMBER LINE AND ORDER Represent, clssify, nd order rel numers. Use inequlities to represent sets of rel numers. Solve inequlities.

More information

Understanding the relationship between floral fragrance, ethylene production and vase life of cut rose flowers

Understanding the relationship between floral fragrance, ethylene production and vase life of cut rose flowers Ethylene, Frgrnce nd Vse Life of Cut Rose Flowers 9/27/216 Progress Report Understnding the reltionship between florl frgrnce, ethylene production nd vse life of cut rose flowers An Mri Bord Dvid Clrk

More information

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block

More information

Acceptance Sampling by Attributes

Acceptance Sampling by Attributes Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire

More information

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn

More information

Supplementary Figure 1 Supplementary Figure 2

Supplementary Figure 1 Supplementary Figure 2 Supplementry Figure 1 Comprtive illustrtion of the steps required to decorte n oxide support AO with ctlyst prticles M through chemicl infiltrtion or in situ redox exsolution. () chemicl infiltrtion usully

More information

Lecture 2: January 27

Lecture 2: January 27 CS 684: Algorithmic Gme Theory Spring 217 Lecturer: Év Trdos Lecture 2: Jnury 27 Scrie: Alert Julius Liu 2.1 Logistics Scrie notes must e sumitted within 24 hours of the corresponding lecture for full

More information

3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression.

3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression. SECTION. Eponents nd Rdicls 7 B 7 7 7 7 7 7 7 NOW TRY EXERCISES 89 AND 9 7. EXERCISES CONCEPTS. () Using eponentil nottion, we cn write the product s. In the epression 3 4,the numer 3 is clled the, nd

More information

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph?

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph? 95. Which of the following descries the net ionic rection for the hydrolysis of NH4Cl( s)? A. NH4 ( q) Cl & ( q) NH4Cl( s) B. NH Cl & 4 ( s) NH4 ( q) Cl ( q) C. Cl ( q) H O & 2 ( l) HCl( q) OH ( q) D.

More information

Chapter 6 Continuous Random Variables and Distributions

Chapter 6 Continuous Random Variables and Distributions Chpter 6 Continuous Rndom Vriles nd Distriutions Mny economic nd usiness mesures such s sles investment consumption nd cost cn hve the continuous numericl vlues so tht they cn not e represented y discrete

More information

Advanced Algebra & Trigonometry Midterm Review Packet

Advanced Algebra & Trigonometry Midterm Review Packet Nme Dte Advnced Alger & Trigonometry Midterm Review Pcket The Advnced Alger & Trigonometry midterm em will test your generl knowledge of the mteril we hve covered since the eginning of the school yer.

More information

The area under the graph of f and above the x-axis between a and b is denoted by. f(x) dx. π O

The area under the graph of f and above the x-axis between a and b is denoted by. f(x) dx. π O 1 Section 5. The Definite Integrl Suppose tht function f is continuous nd positive over n intervl [, ]. y = f(x) x The re under the grph of f nd ove the x-xis etween nd is denoted y f(x) dx nd clled the

More information

Silicon Nanowire Based Single-Molecule SERS Sensor

Silicon Nanowire Based Single-Molecule SERS Sensor Supporting informtion Silicon Nnowire Bsed Single-Molecule SERS Sensor Hui Wng, Xuemei Hn, Xuemei Ou, Chun-Sing Lee, Xiohong Zhng* nd Shuit-Tong Lee S1, A series of Si nnowires coted with compct ggregtes

More information

Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom

Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom Lerning Gols Continuous Rndom Vriles Clss 5, 8.05 Jeremy Orloff nd Jonthn Bloom. Know the definition of continuous rndom vrile. 2. Know the definition of the proility density function (pdf) nd cumultive

More information

Intermediate Math Circles Wednesday, November 14, 2018 Finite Automata II. Nickolas Rollick a b b. a b 4

Intermediate Math Circles Wednesday, November 14, 2018 Finite Automata II. Nickolas Rollick a b b. a b 4 Intermedite Mth Circles Wednesdy, Novemer 14, 2018 Finite Automt II Nickols Rollick nrollick@uwterloo.c Regulr Lnguges Lst time, we were introduced to the ide of DFA (deterministic finite utomton), one

More information

MATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs

MATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs MATHS NOTES The Institute of Eduction 06 SUBJECT: Mths LEVEL: Higher TEACHER: Aidn Rontree Topics Covered: Powers nd Logs About Aidn: Aidn is our senior Mths techer t the Institute, where he hs been teching

More information

Topics Covered AP Calculus AB

Topics Covered AP Calculus AB Topics Covered AP Clculus AB ) Elementry Functions ) Properties of Functions i) A function f is defined s set of ll ordered pirs (, y), such tht for ech element, there corresponds ectly one element y.

More information

Alg. Sheet (1) Department : Math Form : 3 rd prep. Sheet

Alg. Sheet (1) Department : Math Form : 3 rd prep. Sheet Ciro Governorte Nozh Directorte of Eduction Nozh Lnguge Schools Ismili Rod Deprtment : Mth Form : rd prep. Sheet Alg. Sheet () [] Find the vlues of nd in ech of the following if : ) (, ) ( -5, 9 ) ) (,

More information

( ) where f ( x ) is a. AB/BC Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).

( ) where f ( x ) is a. AB/BC Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x). AB/ Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 Find the intersection of f ( x) nd g( x). A3 Show tht f ( x) is even. A4 Show tht

More information

Sample Problems for the Final of Math 121, Fall, 2005

Sample Problems for the Final of Math 121, Fall, 2005 Smple Problems for the Finl of Mth, Fll, 5 The following is collection of vrious types of smple problems covering sections.8,.,.5, nd.8 6.5 of the text which constitute only prt of the common Mth Finl.

More information

5: The Definite Integral

5: The Definite Integral 5: The Definite Integrl 5.: Estimting with Finite Sums Consider moving oject its velocity (meters per second) t ny time (seconds) is given y v t = t+. Cn we use this informtion to determine the distnce

More information

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1 Mth 33 Volume Stewrt 5.2 Geometry of integrls. In this section, we will lern how to compute volumes using integrls defined by slice nlysis. First, we recll from Clculus I how to compute res. Given the

More information

Math 0230 Calculus 2 Lectures

Math 0230 Calculus 2 Lectures Mth Clculus Lectures Chpter 7 Applictions of Integrtion Numertion of sections corresponds to the text Jmes Stewrt, Essentil Clculus, Erly Trnscendentls, Second edition. Section 7. Ares Between Curves Two

More information

MIXED MODELS (Sections ) I) In the unrestricted model, interactions are treated as in the random effects model:

MIXED MODELS (Sections ) I) In the unrestricted model, interactions are treated as in the random effects model: 1 2 MIXED MODELS (Sections 17.7 17.8) Exmple: Suppose tht in the fiber breking strength exmple, the four mchines used were the only ones of interest, but the interest ws over wide rnge of opertors, nd

More information

Jackson 2.26 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell

Jackson 2.26 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell Jckson 2.26 Homework Problem Solution Dr. Christopher S. Bird University of Msschusetts Lowell PROBLEM: The two-dimensionl region, ρ, φ β, is bounded by conducting surfces t φ =, ρ =, nd φ = β held t zero

More information

Homework Assignment 3 Solution Set

Homework Assignment 3 Solution Set Homework Assignment 3 Solution Set PHYCS 44 6 Ferury, 4 Prolem 1 (Griffiths.5(c The potentil due to ny continuous chrge distriution is the sum of the contriutions from ech infinitesiml chrge in the distriution.

More information

2. VECTORS AND MATRICES IN 3 DIMENSIONS

2. VECTORS AND MATRICES IN 3 DIMENSIONS 2 VECTORS AND MATRICES IN 3 DIMENSIONS 21 Extending the Theory of 2-dimensionl Vectors x A point in 3-dimensionl spce cn e represented y column vector of the form y z z-xis y-xis z x y x-xis Most of the

More information

DIRECT CURRENT CIRCUITS

DIRECT CURRENT CIRCUITS DRECT CURRENT CUTS ELECTRC POWER Consider the circuit shown in the Figure where bttery is connected to resistor R. A positive chrge dq will gin potentil energy s it moves from point to point b through

More information

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of

More information

Industrial Electrical Engineering and Automation

Industrial Electrical Engineering and Automation CODEN:LUTEDX/(TEIE-719)/1-7/(7) Industril Electricl Engineering nd Automtion Estimtion of the Zero Sequence oltge on the D- side of Dy Trnsformer y Using One oltge Trnsformer on the D-side Frncesco Sull

More information

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write

More information

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK 11 WRITTEN EXAMINATION 2 SOLUTIONS SECTION 1 MULTIPLE CHOICE QUESTIONS

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK 11 WRITTEN EXAMINATION 2 SOLUTIONS SECTION 1 MULTIPLE CHOICE QUESTIONS MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK WRITTEN EXAMINATION SOLUTIONS FOR ERRORS AND UPDATES, PLEASE VISIT WWW.TSFX.COM.AU/MC-UPDATES SECTION MULTIPLE CHOICE QUESTIONS QUESTION QUESTION

More information

than 1. It means in particular that the function is decreasing and approaching the x-

than 1. It means in particular that the function is decreasing and approaching the x- 6 Preclculus Review Grph the functions ) (/) ) log y = b y = Solution () The function y = is n eponentil function with bse smller thn It mens in prticulr tht the function is decresing nd pproching the

More information

Chapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis

Chapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis Chpter 4: Techniques of Circuit Anlysis Terminology Node-Voltge Method Introduction Dependent Sources Specil Cses Mesh-Current Method Introduction Dependent Sources Specil Cses Comprison of Methods Source

More information

1B40 Practical Skills

1B40 Practical Skills B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need

More information

Polynomial Approximations for the Natural Logarithm and Arctangent Functions. Math 230

Polynomial Approximations for the Natural Logarithm and Arctangent Functions. Math 230 Polynomil Approimtions for the Nturl Logrithm nd Arctngent Functions Mth 23 You recll from first semester clculus how one cn use the derivtive to find n eqution for the tngent line to function t given

More information

Supplementary material

Supplementary material 10.1071/FP11237_AC CSIRO 2012 Accessory Puliction: Functionl Plnt Biology 2012, 39(5), 379 393. Supplementry mteril Tle S1. Effect of wter regime nd genotype on different growth prmeters: spike dry mtter

More information